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Depowdering of lattice structures manufactured by Electron Beam Melting
Aurélien Carré, Matthieu Museau, Pierre-Thomas Doutre
To cite this version:
Aurélien Carré, Matthieu Museau, Pierre-Thomas Doutre. Depowdering of lattice structures manu-
factured by Electron Beam Melting. 15ème Colloque National AIP-Priméca, Apr 2017, La Plagne,
France. �hal-01520004�
Depowdering of lattice structures manufactured by Electron Beam Melting
Aurélien Carré
Univ. Savoie Mont Blanc, SYMME, F-74000 Annecy, France [email protected]
Matthieu Museau
Univ. Grenoble Alpes, CNRS, G-SCOP 38000 Grenoble, France [email protected]
Pierre-Thomas Doutre Univ. Grenoble Alpes, CNRS, G-SCOP
38000 Grenoble, France
[email protected]
Abstract— After completing a part in Electron Beam Melting (EBM), a depowdering operation is required to separate the sintered but unmelted powder from the manufactured part.
Depowdering lattice structures can be difficult or even impossible due to their intrinsic shape. The aim of this paper is to propose a criterion to ensure that a lattice structure manufactured by EBM can be depowdered. The objective is to use this criterion during the design phase of lattice structure to design manufacturable and depowderable parts. Experiments are conducted on depowdering octet-truss lattice structures with variable bars thickness and mesh size. Different criteria are introduced, among them the criterion
"hydraulic diameter" of a lattice structure, inspired by the Darcy- Weisbach hydraulic law used to calculate the pressure drop in a pipe. This criterion can be determined using geometrical characteristics of the lattice structures available in the CAD model of the part. Results show that the levels of depowdering for the lattice structures are proportional to this criterion.
Keywords— electron beam melting, lattice structures, depowdering, powder recovery system.
I. I NTRODUCTION
Nowadays, with the emergence of additive manufacturing processes [1], complex shape [2] that respondent at precise functional criteria can be produced [3]. We therefore want to push the limits in terms of design and optimization of parts, seeking to obtain the best possible shapes [4]. One way to achieve this goal is to use lattice structures that make possible to manufacture products lighter in weight with acceptable mechanical properties [5].
Electron Beam Melting (EBM) is an additive manufacturing process used for producing metal parts and has the potential to manufacture lattice structure with fine features [6]. EBM is a "powder bed" additive manufacturing process:
the part is built layer-by-layer by the melting of metal powder using a powerful electron beam [7][8]. For each layer, the metal powder is spread on a plate by a rake, is sintered by the electron beam to increase thermal and electrical conductivity and is locally melted to produce the required part. Then the
plate goes down of the value of a layer (50 µm) and the cycle is repeated.
Figure 1. A
RCHITECTURE OF ANEBM
MACHINEAt the end of the EBM process, the part is included in a
"cake" of sintered powder. This powder has to be removed to obtain the final part and is then recycled. To perform this depowdering operation, a Powder Recovery System (PRS) [9]
is used: the "cake" of sintered powder containing the manufactured part is blasted with metal powder under 5 bar air pressure [10]. The removed powder is then sieved, so it can be reused. Depowdering lattice structures can be difficult or even impossible due to their intrinsic shape. The aim of this paper is to propose a criterion to ensure that a lattice structure manufactured by EBM can be depowdered. The objective is to use this criterion during the design phase of lattice structure to design manufacturable and depowderable parts.
II. P RELIMINARY DATA - METHODS A. Presentation of the structures
The parts that are studied here are those with lattice
structure. There are various geometries of lattice structures
(diamond, octet-truss, dodecahedron...) with different
properties [11][12]. Our study will deal particularly with octet-
truss: this type of lattice is the best compromise in terms of
mechanical properties [13].
The lattice structures are made by a unit cell that is repeated in the three directions (Figure 2). Three parameters define this cell: the mesh size p, the bars thickness e, and the density of the lattice structure in percentage. One parameter is given by the value of the two others, so only two of them must be chosen.
Figure 2. U
NIT CELL(
ABOVE)
AND LATTICE STRUCTURE(
BELOW) The CAD is realized thanks to a macro [15] that creates a cell with fixed p and e, and then this cell is repeated in the three directions. The manufacturing is prepared with Magics software [16] that allows to place and to orientate the parts on the support plate, and to take into account correcting coefficients due to thermal constraints during manufacturing (the geometry is not affected by any electrical effects).
The hypotheses taken and the boundaries of this study are:
— The structure density must be the same than the cell density; so the number of repetitions of the cell in the three directions must be an integer,
— The standard parameters of the EBM machine are used for the manufacturing of the part,
— Depowdering is studied only in one direction: the removed powder has to go out of the structure through the depowdered face. In that goal, the parts will have a "skin" on five faces, and the last one will be open (Figure 2, bottom right). This makes the worst case, because in a real case with an open lattice, the powder will go out through all faces, and the depowdering would be easier,
— The PRS system is used to depowder the parts, with a pressure of 5 bars, which is the lowest value that is commonly used. The depowdering is done during 3 minutes: some studies show that it permits to remove more than 90% of the consolidated powder [10]
The structures studied can be divided in three groups: the first is composed of 8 unit structures (the unit cell is only repeated in the height), and 12 lattice structures (the unit cell is repeated in the three directions) with mesh sizes between 4 mm and 15 mm. Those 20 parts have a density of 25%: this value is the best compromise between a light structure and a good
rigidity, and allows a large choice of mesh size and bars thickness. The width of the lattice structures are 24, 30 and 36 mm, and the heights of the 20 parts are from 48 mm to 63 mm, to satisfy the hypothesis of an integer number of repetitions.
The second group is composed of 8 square cylinders, with a width between 4 mm and 15 mm, and a height of 49 mm (for a comparison with available data on depowdering circular cylinders [10][14]).
In the third group, there are 22 lattice structures with a density between 3% and 66% and mesh sizes between 4 mm and 12 mm. The width and the height are 24 and 30 mm. Those parts will permit to have a larger range of results.
B. Calculation of the depowdered height
Each part is weighed before and after depowdering: so the initial mass 𝑚𝑚
𝑖𝑖and the final mass 𝑚𝑚
𝑓𝑓are known.
For the square cylinders, the depowdered height is calculated as follows, with S the hollow section and 𝜌𝜌
𝑐𝑐the density of the consolidated powder:
éq. (1) ℎ
𝑑𝑑=
𝑚𝑚𝑆𝑆.𝜌𝜌𝑖𝑖−𝑚𝑚𝑓𝑓𝑐𝑐
For the lattices, the structure is more complex. In particular, the 1 mm thick skin is extended around the open face, to create a step that permits not to begin the lattice on the start plate.
Figure 3. D
ATA FOR THE CALCULATIONFor calculations, ℎ
𝑡𝑡is the lattice height, S the lattice section, 𝑉𝑉
𝑝𝑝,𝑖𝑖the initial volume of consolidated powder in the whole structure (determined by CAD) and 𝑉𝑉
𝑝𝑝𝑝𝑝,𝑖𝑖the usefull initial volume of consolidated powder. It’s determined with:
éq. (2) 𝑉𝑉
𝑝𝑝,𝑖𝑖= 𝑆𝑆 × 1 + 𝑉𝑉
𝑝𝑝𝑝𝑝,𝑖𝑖The final volume of powder, after depowdering, is 𝑉𝑉
𝑝𝑝,𝑓𝑓. Thereby:
éq. (3) 𝑚𝑚
𝑖𝑖− 𝑚𝑚
𝑓𝑓= �𝑉𝑉
𝑝𝑝,𝑖𝑖− 𝑉𝑉
𝑝𝑝,𝑓𝑓�. 𝜌𝜌
𝑐𝑐= �𝑆𝑆 × 1 + 𝑉𝑉
𝑝𝑝𝑝𝑝,𝑖𝑖− 𝑉𝑉
𝑝𝑝,𝑓𝑓�. 𝜌𝜌
𝑐𝑐The depowdered height h
dis calculated as follows:
éq. (4)
ℎ𝑑𝑑ℎ𝑡𝑡
=
ℎ𝑡𝑡−ℎ𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑖𝑖𝑟𝑟𝑖𝑖𝑟𝑟𝑔𝑔ℎ𝑡𝑡
=
𝑉𝑉𝑝𝑝𝑝𝑝,𝑖𝑖𝑉𝑉−𝑉𝑉𝑝𝑝,𝑓𝑓𝑝𝑝𝑝𝑝,𝑖𝑖
Then:
éq. (5) 𝑚𝑚
𝑖𝑖− 𝑚𝑚
𝑓𝑓= �𝑆𝑆 × 1 +
ℎℎ𝑑𝑑𝑡𝑡
𝑉𝑉
𝑝𝑝𝑝𝑝,𝑖𝑖� . 𝜌𝜌
𝑐𝑐= �𝑆𝑆 × 1 + ℎ
𝑑𝑑ℎ
𝑡𝑡. �𝑉𝑉
𝑝𝑝,𝑖𝑖− 𝑆𝑆 × 1�� . 𝜌𝜌
𝑐𝑐The depowdered height can be determined:
éq. (6) ℎ
𝑑𝑑= �
𝑚𝑚𝑖𝑖𝜌𝜌−𝑚𝑚𝑓𝑓𝑐𝑐
− 𝑆𝑆 × 1� .
𝑉𝑉 ℎ𝑡𝑡𝑝𝑝,𝑖𝑖−𝑆𝑆×1
The calculated values are verified fore some parts, by dipping a thin iron wire and measuring the depth.
In order to predict the depowdered height in a structure, five different criteria are defined and then tested. Three of them are related to the free surface, and two of them to the hydraulic diameter. They are presented in the following of this paper.
III. F REE SURFACE A. Criteria
The free surface 𝑆𝑆
𝑙𝑙in a structure is defined at different heights, as the portion of the surface without material. It can be determined thanks to a CAD software, because the occupied surface 𝑆𝑆
𝑜𝑜𝑐𝑐𝑐𝑐(portion of the surface with material) is measurable: 𝑆𝑆
𝑙𝑙= (𝑛𝑛𝑛𝑛)
2− 𝑆𝑆
𝑜𝑜𝑐𝑐𝑐𝑐, with p the mesh size and n the number of repetitions of the cell in the plan. For a 24 mm width octet-truss structure with p = 12 mm, the evolution of the free surface is represented in the following figure:
Figure 4. F
REE SURFACE FONCTION OF THE HEIGHT OF CUTThe trend is the same for every octet-truss lattice, with a number of waves depending on the number of repetitions in the direction of depowdering.
From this point, it is possible to define three criteria that could be related to the depowdered height:
— The minimum free surface: min( 𝑆𝑆
𝑙𝑙). In an octet-truss, it occurs in the open face, and can block the powder projection,
— The average free surface: moy( 𝑆𝑆
𝑙𝑙). It can’t describe the sudden variations, but it represents the free surface in global,
— The gap between maximum and minimum of free surface: max( 𝑆𝑆
𝑙𝑙) - min( 𝑆𝑆
𝑙𝑙). It highlights the maximum variation in all the profile.
B. Results
Those criteria are calculated for all parts of the group 1 and 2. The relation between the depowdered height and each
criterion can be represented on a graphic. Only the graphic for the minimum of free surface is showed here, because for the other criteria it presents the same characteristics. The parts are divided in five colors, to better see the specificities of each type.
Figure 5. D
EPOWDERED HEIGHT FUNCTION OF THE MINIMUM OF FREE SURFACEFor the square cylinders and the unit structures, the criterion could be interesting because it reveals a linear relation with the depowdered height. Nevertheless, the most important results are about the lattice structures. For a certain size of lattice (24 mm, 30 mm and 36 mm), the minimum of free surface is the same for different mesh sizes. For the two other criteria, the conclusion is the same: the value of the criteria is equal for different mesh sizes.
It shows that these three criteria are not valid to predict the depowdered height: for example, if the value of the minimum of free surface is known, it’s impossible to determine the height of powder that will be removed. With the same minimum of free surface, the depowdered height that is predicted can range from simple to triple. Finally, the criteria based only on the free surface can’t be used to determine the powder that could be depowdered on a random lattice structure.
In the following part, other criteria are proposed to fulfill the initial objective.
IV. H YDRAULIC DIAMETER A. Criteria
The depowdering stage can be seen as a pressure drop: the pressure due to the blasting is maximum at the open face, and is at the atmospherical pressure where the depowdering is stopped, at the bottom of the lattice.
In a general case in hydraulic, the pressure drops ∆𝑛𝑛 in canals are calculated with the Darcy-Weisbach law [17]:
éq. (7) ∆𝑛𝑛 = 𝑓𝑓
𝐷𝐷𝐷𝐷𝐿𝐿ℎ 𝜌𝜌𝑣𝑣2
2
With 𝑓𝑓
𝐷𝐷the pressure drop coefficient, L the canal length, 𝜌𝜌 the density, 𝑣𝑣 the speed of the fluid, and 𝐷𝐷
ℎthe hydraulic diameter, given by:
éq. (8) 𝐷𝐷
ℎ=
4𝑆𝑆𝑃𝑃𝑟𝑟𝑟𝑟
With 𝑆𝑆
𝑚𝑚the wetted area and 𝑃𝑃
𝑚𝑚the wetted perimeter.
This theory is applied to lattice structures: the goal is not to valid the Darcy-Weisbach law for those structures, but to make an analogy to find a possible rule about depowdering. The depowdered height that is researched corresponds to the length L that is renamed ℎ
𝑑𝑑. It can be determined with the previous formula (éq. (7)):
éq. (9) ℎ
𝑑𝑑= 𝐿𝐿 = ∆𝑛𝑛
𝑓𝑓1𝐷𝐷 2 𝜌𝜌𝑣𝑣2
